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        <p>kmp算法原理和实现，转自：<a href="https://blog.csdn.net/v_july_v/article/details/7041827" target="_blank" rel="noopener">从头到尾彻底理解KMP（2014年8月22日版）</a>。</p>
<a id="more"></a>
<h1 id="暴力算法"><a href="#暴力算法" class="headerlink" title="暴力算法"></a>暴力算法</h1><p>假设现在我们面临这样一个问题：有一个文本串S，和一个模式串P，现在要查找P在S中的位置，怎么查找？</p>
<p>如果用暴力算法的思路，并假设现在文本串S匹配到$i$，模式串P匹配到$j$位置，则有：</p>
<ul>
<li>如果当前字符串串匹配成功，即$S[i]==p[j]$，则$i++,j++$，继续匹配下一个字符；</li>
<li>如果失败，即$S[i] != P[j]$，则令<code>i=i-(j-1),j=0</code>，相等于每次匹配失败时，$i$回溯，$j$被重置为0。</li>
</ul>
<p>代码实现：</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;string&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">strMatch</span><span class="params">(<span class="built_in">string</span> &amp; S, <span class="built_in">string</span> &amp; P)</span> </span>&#123;</span><br><span class="line">	<span class="keyword">if</span> (S.empty() || P.empty())</span><br><span class="line">		<span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">	<span class="keyword">int</span> i = <span class="number">0</span>, j = <span class="number">0</span>;</span><br><span class="line">	<span class="keyword">while</span> (j &lt; P.size() &amp;&amp; i &lt; S.size()) &#123;</span><br><span class="line">		<span class="keyword">if</span> (S[i] == P[j]) &#123;</span><br><span class="line">			++i, ++j;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">else</span> &#123;</span><br><span class="line">			i = i - (j - <span class="number">1</span>);</span><br><span class="line">			j = <span class="number">0</span>;</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">return</span> i - j;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span> </span>&#123;</span><br><span class="line">	<span class="built_in">string</span> S = <span class="string">"abcdefgad"</span>, P = <span class="string">"defga"</span>;</span><br><span class="line">	<span class="built_in">cout</span> &lt;&lt; strMatch(S, P) &lt;&lt; <span class="built_in">endl</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>还有变形，求模式串P是否在模式串S中存在，可以通过动态规划实现：</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;vector&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;string&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">strMatch</span><span class="params">(<span class="built_in">string</span> &amp; S, <span class="built_in">string</span> &amp; P)</span> </span>&#123;</span><br><span class="line">	<span class="keyword">if</span> (S.empty() || P.empty())</span><br><span class="line">		<span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">	<span class="keyword">int</span> lenS = S.size(), lenP = P.size();</span><br><span class="line">	<span class="built_in">vector</span>&lt;<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt;&gt; dp(lenS+<span class="number">1</span>, <span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt;(lenP+<span class="number">1</span>, <span class="number">0</span>));</span><br><span class="line">	dp[<span class="number">0</span>][<span class="number">0</span>] = <span class="number">0</span>;</span><br><span class="line">	<span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">1</span>; i &lt;= lenS; ++i) &#123;</span><br><span class="line">		dp[i][<span class="number">0</span>] = <span class="number">0</span>;</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">for</span> (<span class="keyword">int</span> j = <span class="number">1</span>; j &lt;= lenP; ++j) &#123;</span><br><span class="line">		dp[<span class="number">0</span>][j] = <span class="number">0</span>;</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">1</span>; i &lt;= lenS; ++i) &#123;</span><br><span class="line">		<span class="keyword">for</span> (<span class="keyword">int</span> j = <span class="number">1</span>; j &lt;= lenP; ++j) &#123;</span><br><span class="line">			<span class="keyword">if</span> (S[i - <span class="number">1</span>] == P[j - <span class="number">1</span>]) &#123;</span><br><span class="line">				dp[i][j] = dp[i - <span class="number">1</span>][j - <span class="number">1</span>] + <span class="number">1</span>;</span><br><span class="line">			&#125;</span><br><span class="line">			<span class="keyword">else</span> &#123;</span><br><span class="line">				dp[i][j] = max(dp[i - <span class="number">1</span>][j], dp[i][j - <span class="number">1</span>]);</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">return</span> dp[lenS][lenP];</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span> </span>&#123;</span><br><span class="line">	<span class="built_in">string</span> S = <span class="string">"abcdefgad"</span>, P = <span class="string">"defga"</span>;</span><br><span class="line">	<span class="built_in">cout</span> &lt;&lt; strMatch(S, P) &lt;&lt; <span class="built_in">endl</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>以上两种实现的时间复杂度都是$o(n)$。</p>
<p>举个例子，如果给定文本串S“BBC ABCDAB ABCDABCDABDE”，和模式串P“ABCDABD”，现在要拿模式串P去跟文本串S匹配，整个过程如下所示：</p>
<ol>
<li><p>S[0]为B，P[0]为A，不匹配，执行第②条指令：“如果失配（即S[i]! = P[j]），令i = i - (j - 1)，j = 0”，S[1]跟P[0]匹配，相当于模式串要往右移动一位（i=1，j=0）</p>
<p><a href="http://image.rexking6.top/img/clip1586225297.png" target="_blank" rel="noopener"><img src="http://image.rexking6.top/img/clip1586225297.png" alt="img"></a></p>
</li>
<li><p>S[1]跟P[0]还是不匹配，继续执行第②条指令：“如果失配（即S[i]! = P[j]），令i = i - (j - 1)，j = 0”，S[2]跟P[0]匹配（i=2，j=0），从而模式串不断的向右移动一位（不断的执行“令i = i - (j - 1)，j = 0”，i从2变到4，j一直为0）<br><a href="http://image.rexking6.top/img/clip1586225316.png" target="_blank" rel="noopener"><img src="http://image.rexking6.top/img/clip1586225316.png" alt="img"></a></p>
</li>
<li><p>直到S[4]跟P[0]匹配成功（i=4，j=0），此时按照上面的暴力匹配算法的思路，转而执行第①条指令：“如果当前字符匹配成功（即S[i] == P[j]），则i++，j++”，可得S[i]为S[5]，P[j]为P[1]，即接下来S[5]跟P[1]匹配（i=5，j=1）</p>
<p><a href="http://image.rexking6.top/img/clip1586225332.png" target="_blank" rel="noopener"><img src="http://image.rexking6.top/img/clip1586225332.png" alt="img"></a></p>
</li>
<li><p>S[5]跟P[1]匹配成功，继续执行第①条指令：“如果当前字符匹配成功（即S[i] == P[j]），则i++，j++”，得到S[6]跟P[2]匹配（i=6，j=2），如此进行下去</p>
<p><a href="http://image.rexking6.top/img/clip1586225348.png" target="_blank" rel="noopener"><img src="http://image.rexking6.top/img/clip1586225348.png" alt="img"></a></p>
</li>
<li><p>直到S[10]为空格字符，P[6]为字符D（i=10，j=6），因为不匹配，重新执行第②条指令：“如果失配（即S[i]! = P[j]），令i = i - (j - 1)，j = 0”，相当于S[5]跟P[0]匹配（i=5，j=0）</p>
<p><a href="http://image.rexking6.top/img/clip1586225365.png" target="_blank" rel="noopener"><img src="http://image.rexking6.top/img/clip1586225365.png" alt="img"></a></p>
</li>
<li><p>至此，我们可以看到，如果按照暴力匹配算法的思路，尽管之前文本串和模式串已经分别匹配到了S[9]、P[5]，但因为S[10]跟P[6]不匹配，所以文本串回溯到S[5]，模式串回溯到P[0]，从而让S[5]跟P[0]匹配。</p>
<p><a href="http://image.rexking6.top/img/clip1586225380.png" target="_blank" rel="noopener"><img src="http://image.rexking6.top/img/clip1586225380.png" alt="img"></a></p>
</li>
</ol>
<p>而S[5]肯定跟P[0]失配。为什么呢？因为在之前第4步匹配中，我们已经得知S[5] = P[1] = B，而P[0] = A，即P[1] != P[0]，故S[5]必定不等于P[0]，所以回溯过去必然会导致失配。那有没有一种算法，让i 不往回退，只需要移动j 即可呢？</p>
<p>答案是肯定的。这种算法就是本文的主旨KMP算法，它利用之前已经部分匹配这个有效信息，保持i 不回溯，通过修改j 的位置，让模式串尽量地移动到有效的位置。</p>
<h1 id="KMP算法"><a href="#KMP算法" class="headerlink" title="KMP算法"></a>KMP算法</h1><p>KMP主要分为三个步骤：</p>
<ul>
<li>构造前缀表，即prefix table</li>
<li>前缀表后移，并将第一个元素置为-1</li>
<li>KMP查找主体</li>
</ul>
<p>对于前缀表的的构造：</p>
<p>最终需要的结果：</p>
<p><img src="https://raw.githubusercontent.com/zxpgo/images/master/img/20200426184455.png" alt=""></p>
<p>实现的具体思路：</p>
<p>通过观察发现上面的表格，ABABCA的最长公共前后缀的长度为1，最左边的字母和最右边的字母相同。要想公共前后缀长度变长，变成2。唯一的做法在字符串末尾添加一个跟第二字母相同的字母。可以发现前后字符串的最长公共前后缀是有关系的。</p>
<p><img src="https://raw.githubusercontent.com/zxpgo/images/master/img/20200426185030.png" alt=""></p>
<p>如果<code>pattern[i] == pattern[len]</code>，表示最长公共前后缀的长度需要加1。</p>
<p><img src="https://raw.githubusercontent.com/zxpgo/images/master/img/20200426184302.png" alt=""></p>
<p>前缀表(prefix table)代码实现：</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br></pre></td><td class="code"><pre><span class="line"><span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; prefix_table(<span class="built_in">string</span> &amp; pattern) &#123;</span><br><span class="line">	<span class="keyword">int</span> n = pattern.size();</span><br><span class="line">	<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; prefix(n);</span><br><span class="line">	prefix[<span class="number">0</span>] = <span class="number">0</span>;</span><br><span class="line">	<span class="keyword">int</span> len = <span class="number">0</span>, i = <span class="number">1</span>;</span><br><span class="line">	<span class="keyword">while</span>(i &lt; n) &#123;</span><br><span class="line">		<span class="keyword">if</span> (pattern[len] == pattern[i]) &#123;</span><br><span class="line">			++len;</span><br><span class="line">			prefix[i] = len;</span><br><span class="line">			++i;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">else</span> &#123;</span><br><span class="line">			<span class="keyword">if</span> (len &gt; <span class="number">0</span>) &#123;</span><br><span class="line">				len = prefix[len - <span class="number">1</span>];</span><br><span class="line">			&#125;</span><br><span class="line">			<span class="keyword">else</span> &#123;</span><br><span class="line">				prefix[i] = len; <span class="comment">//len=0</span></span><br><span class="line">				++i;</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line"></span><br><span class="line">	<span class="keyword">return</span> prefix;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">move_prefix_table</span><span class="params">(<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; &amp; table)</span> </span>&#123;</span><br><span class="line">	<span class="keyword">for</span> (<span class="keyword">int</span> i = table.size() - <span class="number">1</span>; i &gt; <span class="number">0</span>; --i) &#123;</span><br><span class="line">		table[i] = table[i<span class="number">-1</span>];</span><br><span class="line">	&#125;</span><br><span class="line">	table[<span class="number">0</span>] = <span class="number">-1</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>KMP算法实现：</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">kmp_search</span><span class="params">(<span class="built_in">string</span> &amp; S, <span class="built_in">string</span> &amp; P)</span> </span>&#123;</span><br><span class="line">	<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; prefix = prefix_table(P);</span><br><span class="line">	move_prefix_table(prefix);</span><br><span class="line"></span><br><span class="line">	<span class="comment">//S[i] lenS</span></span><br><span class="line">	<span class="comment">//P[j] lenP</span></span><br><span class="line">	<span class="keyword">int</span> i = <span class="number">0</span>, j = <span class="number">0</span>;</span><br><span class="line">	<span class="keyword">int</span> lenS = S.size(), lenP = P.size();</span><br><span class="line">	<span class="keyword">while</span> (i &lt; lenS) &#123;</span><br><span class="line">		<span class="keyword">if</span> (j == lenP - <span class="number">1</span> &amp;&amp; S[i] == P[j]) &#123;</span><br><span class="line">			<span class="built_in">cout</span> &lt;&lt; <span class="string">"Found pattern at "</span> &lt;&lt; i - j &lt;&lt; <span class="built_in">endl</span>;</span><br><span class="line">			j = prefix[j];</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">if</span> (S[i] == P[j]) &#123;</span><br><span class="line">			++i, ++j;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">else</span> &#123;</span><br><span class="line">			j = prefix[j];</span><br><span class="line">			<span class="keyword">if</span> (j == <span class="number">-1</span>) &#123;</span><br><span class="line">				++i, ++j;</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>完整的代码：</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;string&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;vector&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"></span><br><span class="line"><span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; prefix_table(<span class="built_in">string</span> &amp; pattern) &#123;</span><br><span class="line">	<span class="keyword">int</span> n = pattern.size();</span><br><span class="line">	<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; prefix(n);</span><br><span class="line">	prefix[<span class="number">0</span>] = <span class="number">0</span>;</span><br><span class="line">	<span class="keyword">int</span> len = <span class="number">0</span>, i = <span class="number">1</span>;</span><br><span class="line">	<span class="keyword">while</span>(i &lt; n) &#123;</span><br><span class="line">		<span class="keyword">if</span> (pattern[len] == pattern[i]) &#123;</span><br><span class="line">			++len;</span><br><span class="line">			prefix[i] = len;</span><br><span class="line">			++i;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">else</span> &#123;</span><br><span class="line">			<span class="keyword">if</span> (len &gt; <span class="number">0</span>) &#123;</span><br><span class="line">				len = prefix[len - <span class="number">1</span>];</span><br><span class="line">			&#125;</span><br><span class="line">			<span class="keyword">else</span> &#123;</span><br><span class="line">				prefix[i] = len; <span class="comment">//len=0</span></span><br><span class="line">				++i;</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line"></span><br><span class="line">	<span class="keyword">return</span> prefix;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">move_prefix_table</span><span class="params">(<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; &amp; table)</span> </span>&#123;</span><br><span class="line">	<span class="keyword">for</span> (<span class="keyword">int</span> i = table.size() - <span class="number">1</span>; i &gt; <span class="number">0</span>; --i) &#123;</span><br><span class="line">		table[i] = table[i<span class="number">-1</span>];</span><br><span class="line">	&#125;</span><br><span class="line">	table[<span class="number">0</span>] = <span class="number">-1</span>;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">kmp_search</span><span class="params">(<span class="built_in">string</span> &amp; S, <span class="built_in">string</span> &amp; P)</span> </span>&#123;</span><br><span class="line">	<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; prefix = prefix_table(P);</span><br><span class="line">	move_prefix_table(prefix);</span><br><span class="line"></span><br><span class="line">	<span class="comment">//S[i] lenS</span></span><br><span class="line">	<span class="comment">//P[j] lenP</span></span><br><span class="line">	<span class="keyword">int</span> i = <span class="number">0</span>, j = <span class="number">0</span>;</span><br><span class="line">	<span class="keyword">int</span> lenS = S.size(), lenP = P.size();</span><br><span class="line">	<span class="keyword">while</span> (i &lt; lenS) &#123;</span><br><span class="line">		<span class="keyword">if</span> (j == lenP - <span class="number">1</span> &amp;&amp; S[i] == P[j]) &#123;</span><br><span class="line">			<span class="built_in">cout</span> &lt;&lt; <span class="string">"Found pattern at "</span> &lt;&lt; i - j &lt;&lt; <span class="built_in">endl</span>;</span><br><span class="line">			j = prefix[j];</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">if</span> (S[i] == P[j]) &#123;</span><br><span class="line">			++i, ++j;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">else</span> &#123;</span><br><span class="line">			j = prefix[j];</span><br><span class="line">			<span class="keyword">if</span> (j == <span class="number">-1</span>) &#123;</span><br><span class="line">				++i, ++j;</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span> </span>&#123;</span><br><span class="line">	<span class="built_in">string</span> S = <span class="string">"ABABABABCABAABABABCABAA"</span>, P = <span class="string">"ABABCABAA"</span>;</span><br><span class="line">	<span class="built_in">vector</span>&lt;<span class="keyword">int</span>&gt; table = prefix_table(P);</span><br><span class="line">	move_prefix_table(table);</span><br><span class="line">	<span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; table.size(); ++i)</span><br><span class="line">		<span class="built_in">cout</span> &lt;&lt; table[i] &lt;&lt; <span class="built_in">endl</span>;</span><br><span class="line">	kmp_search(S, P);</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p>参考：</p>
<p>[1] <a href="https://blog.csdn.net/v_july_v/article/details/7041827" target="_blank" rel="noopener">https://blog.csdn.net/v_july_v/article/details/7041827</a></p>
<p>[2] <a href="http://blog.rexking6.top/2017/08/07/KMP算法/" target="_blank" rel="noopener">http://blog.rexking6.top/2017/08/07/KMP%E7%AE%97%E6%B3%95/</a></p>
<p>[3] <a href="https://www.bilibili.com/video/BV1hW411a7ys" target="_blank" rel="noopener">https://www.bilibili.com/video/BV1hW411a7ys</a></p>

      
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</body>
</html>
